In this thesis, the blind source separation (BSS) on digitalaudio signals via background learning by several differentmethodologies is carefully studied. In the daily auditory, acoustic audio signals are usually mixtures of different sources, including foreground andbackground noises. Most of the time, we only want to receive the foregroundsources and get rid of the background ones. Because of the randomness ofvarious situations, it is very difficult to perform this separation without knowing the detailed information. Even if the background noises are not dominating the foreground sources, or even much weaker, it is still a difficult problem, especially for the case that there are more than three sources including the noise. This also makes it even more difficult to separate different sources from mixed signals. In this thesis, a novel approach to solve cancellation kernels is provided by using a modified sigular value decomposition method. The main focus is to use this new technique to estimate the cacellation kernels with good results in short computational time.In this work, some background information for blind source separation of audio will be first introduced. Next, the knowledge of four different methods for solving this type of problems is mentioned. Split Bregman has been studied by others in solving cancellation kernels for the separation of speech signals. We apply proximity operator method to solve the cancellation kernels for BSS of audio signal processing. It has been applied to study image processing by other researchers. Quadratic programming method has been applied to solve cancellation kernels by Wang and Zhou. We provide a new approach to bring sparseness to cancellation kernels by using quadratic programming. We developed a modified singular value decomposition (SVD) algorithm based on the numerical experiments. It is a new technique to estimate cancellation kernels for BSS of audio signals. The detailed information and schemes are presented in Chapter 3. Then, in the fouth chapter, there are different numerical simulation examples according to different scenarios. We compare the results of our modified SVD method with others methods, and conclude that our modified SVD is the best approach.
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